SOLUTION: the volume of a rectangular prism is 96x^3+48x^2+6x. what is its dimensions? using the answer, find an expression that describes the perimeter of one of the prism's faces.

Question 862089: the volume of a rectangular prism is 96x^3+48x^2+6x. what is its dimensions?
using the answer, find an expression that describes the perimeter of one of the prism's faces.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
There is an infinite number of possible answers.
Some are easier to write than others.

Maybe and the prism measures by by .
For that prism, two of the faces will be squares,
measuring by ,
with a perimeter of ,
while the other four faces are rectangles measuring by ,
each with a perimeter of .

It could be that and the prism measures
by by .
In that case there are 3 pairs of faces whose measures are pairs of those dimensions.
Two of the faces will measure by ,
with a perimeter of .
Another pair of faces measures by ,
with perimeters of .
The remaining pair of faces would measure by ,
and would have perimeters equal to .

Maybe the prism is a cube with sides measuring ,
and each of its faces has a perimeter of .

I will not make an infinite list, because I have a finite life, and it's past my bedtime, anyway.
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